Optimal transportation on non-compact manifolds

In this work, we show how to obtain for non-compact manifolds the results that have already been done for Monge Transport Problem for costs coming from Tonelli Lagrangians on compact manifolds. In particular, the already known results for a cost of the type d ^r , r > 1, where d is the Riemannian distance of a complete Riemannian manifold, hold without any curvature restriction.     

An exact, closed-form solution for equilibrium of trveling, sagged, elastic cables under uniformly distributed loading

IntroctionThquilibrium of sagged, elastic cable s under its own weight loading is needed in tiledesign of cable structures. In 1851 RO'htsLll first investigated a uniform, inextensible suspendedchain hanging freely under its own weight. Ro.th[Zj considered a model of a heterogeneouschain hanging in the form of a cycloid, and application of this model to the uniform chainreduced to the Rohrs model when the sag ratio is small. However, the chain was modeled asinextensible. Pugsley['] develope…     

Preface

Foundations of Computational Mathematics -     

Dynamic Environments as a Tool to Preserve Desired Output in a Chemical Reaction Network

Current efforts to design functional molecular systems have overlooked the importance of coupling out-of-equilibrium behaviour with changes in the environment. Here, the authors use an oscillating reaction network and demonstrate that the application of environmental forcing, in the form of periodic changes in temperature and in the inflow of the concentration of one of the network components, removes the dependency of the periodicity of this network on temperature or flow rates and enforces a stable periodicity across a wide range of conditions. Coupling a system to a dynamic environment can thus be used as a simple tool to regulate the output of a network. In addition, the authors show that coupling can also induce an increase in behavioural complexity to include quasi-periodic oscillations.     

Saturable Absorption and Bistable Switching of Single Mode Fiber Core-Guided Light by a 6 nm-thick,Few Layers Graphene Coating on the Cladding Surface

The coupling of less than 80 µW of in-plane polarized near-infrared light in a 6 nm-thick graphene layer deposited on an optical fiber produces important permittivity changes leading to bistability and self-starting 50% modulation of over 1 W of continuous wave light in the core. These features arise from resonant coupling of core-guided light into the cladding by a 12-degree tilted, 1 cm long fiber Bragg grating via narrowband, polarization-dependent resonances that allow the selection of cladding modes with electric fields polarized in the plane of the graphene. The pulse repetition rate of the modulation increases from 10 to 269 Hz for input powers ranging from 0.3 to 1.33 W in the core, with no evidence of saturation. Investigations into the origin of these effects through physical modelling and different experimental conditions point to photo-induced Joule heating in the graphene layer giving rise to temperature increases of the order of 60 °C and corresponding permittivity changes in the graphene and underlying silica fiber. Those changes lead to shifts in the resonance positions which result in the equivalent of saturable absorption for light guided in the core without direct contact with the absorbing graphene layer.     

Synthesis and applications of optically active metallacycles derived from primary amines

The synthesis of optically active cyclopalladated derivatives containing primary amines and their application as resolving agents of Lewis bases is reviewed. Some other applications such as the determination of the absolute configuration of coordinated chiral phosphines and the synthesis of chiral liquid crystals are also presented.     

One-pot synthesis of highly substituted indolines

A general and convenient one-pot synthesis of highly substituted indolines from arylhydrazines and aldehydes is reported. This synthesis allows introduction of substitution at essentially all positions of the indoline nucleus to achieve significant diversity in this biologically important template.     

On Invariant Line Fields

It is shown that a rational function of degree 2 admits aninvariant line field with respect to some measure µ, whichis an equilibrium state of a Hölder continuous potentialwhose topological pressure is greater than its supremum, onlyin very special cases when the Julia set is either a geometriccircle or an interval, or totally disconnected and containedin a real-analytic curve. 1991 Mathematics Subject Classification37F10, 30E99, 28D05, 28D99.